First of all, yes custom textures must be squares such as 64x64; 128x128; 256x256; 512x512; 1024x1024;etc.
JK2 Mapping contains several tutorials among them lifts. http://mapping.jediknightii.net/tutorials.htm
To make teleporters create a brush with the trigger shader and make it into a trigger_teleport over your teleport pad brush and give it these:
Next create a target position in the area where you want to teleport to and give it:
This should link your two entities together. If you don't see a line going between the two then select the trigger first and the target_position second and press CTRL+K to bind the two together. That's all she wrote. Goodluck.